Zobrazeno 1 - 10
of 59
pro vyhledávání: '"Ott, Sébastien"'
We discuss the relaxation time (inverse spectral gap) of the one dimensional $O(N)$ model, for all $N$ and with two types of boundary conditions. We see how its low temperature asymptotic behavior is affected by the topology. The combination of the s
Externí odkaz:
http://arxiv.org/abs/2407.12610
The motivation for this paper is the analysis of the fixed-density Ising lattice gas in the presence of a gravitational field. This is a seen as a particular instance of an Ising model with a slowly varying magnetic field in the fixed magnetization e
Externí odkaz:
http://arxiv.org/abs/2307.03139
Autor:
Ott, Sébastien
Two proofs of the Central Limit Theorem using a renormalization group approach are presented. The first proof is conducted under a third moment assumption and shows that a suitable renormalization group map is a contraction over the space of probabil
Externí odkaz:
http://arxiv.org/abs/2303.13905
Autor:
Giuliani, Alessandro, Ott, Sébastien
We consider classical $O(N)$ vector models in dimension three and higher and investigate the nature of the low-temperature expansions for their multipoint spin correlations. We prove that such expansions define asymptotic series, and derive explicit
Externí odkaz:
http://arxiv.org/abs/2302.07299
Publikováno v:
Commun. Math. Phys. 399, 1103-1138 (2023)
We consider the Random-Cluster model on $\mathbb{Z}^d$ with interactions of infinite range of the form $J_x = \psi(x)\mathsf{e}^{-\rho(x)}$ with $\rho$ a norm on $\mathbb{Z}^d$ and $\psi$ a subexponential correction. We first provide an optimal crite
Externí odkaz:
http://arxiv.org/abs/2207.02193
Publikováno v:
Annales de l'Institut Henri Poincar\'e 60, 167-207 (2024)
We prove Ornstein-Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the interaction. The main contribution of this work is that the
Externí odkaz:
http://arxiv.org/abs/2112.13057
Autor:
Lammers, Piet, Ott, Sébastien
Publikováno v:
Probability Theory and Related Fields (2023)
The solid-on-solid model is a model of height functions, introduced to study the interface separating the $+$ and $-$ phase in the Ising model. The planar solid-on-solid model thus corresponds to the three-dimensional Ising model. Delocalisation of t
Externí odkaz:
http://arxiv.org/abs/2101.05139
Publikováno v:
Annals of Probability 50, 1127-1172 (2022)
In this paper we develop a detailed analysis of critical prewetting in the context of the two-dimensional Ising model. Namely, we consider a two-dimensional nearest-neighbor Ising model in a $2N\times N$ rectangular box with a boundary condition indu
Externí odkaz:
http://arxiv.org/abs/2011.11997
Publikováno v:
Communications in Mathematical Physics 386, 433-467 (2021)
We consider a variety of lattice spin systems (including Ising, Potts and XY models) on $\mathbb{Z}^d$ with long-range interactions of the form $J_x = \psi(x) e^{-|x|}$, where $\psi(x) = e^{\mathsf{o}(|x|)}$ and $|\cdot|$ is an arbitrary norm. We cha
Externí odkaz:
http://arxiv.org/abs/2011.09802
Autor:
Lammers, Piet1 (AUTHOR) lammers@ihes.fr, Ott, Sébastien2 (AUTHOR)
Publikováno v:
Probability Theory & Related Fields. Feb2024, Vol. 188 Issue 1/2, p63-87. 25p.